Find the exact value of following expressions using double-angle formula. Do not use decimals and rationalize the denominator if necessary. 2 tan-) 1- tan (-*)

Q: If 0∘<θ<90∘ and sin⁡θ=2425, find sec⁡θ using trigonometric identities. 725 257 2524 2425

A:

Q: Use addition formulas and the values of sin(ø) and cos(ø) for ø=pi/3 , pi/4 to compute sin(pi/12)…

A: Use formulae: also, make use of:

Q: Using trigonometric substitution to evaluate 2, we will get A (1+ cos20) de what is the value of Az…

A: Given,

Q: Use the sin/cos complementary relationship to determine which of the following expression is also…

A:

Q: Use the power-reducing formulas to rewrite the expression 6 sin4 x as an equivalent expression that…

A: We have to use the power-reducing formulas to rewrite the expression 6 sin4x as an equivalent…

Q: Use a right triangle to simplify the given expression as shown. Assume x 7 0.

A:

Q: Rewrite the expression as an equivalent expression that does not contain powers of trigonometric…

A:

Q: Write an equivalent expression for sin4 x that does not contain powers of trigonometric functions…

A:

Q: Evaluate the following so that no trigonometric functions remain: cos ( tan'

A: Consider the given trigonometric function. costan-11x The objective of the problem is to evaluate…

Q: Simplify using either an Addition / Subtraction Formula or a Double Angle Formula, and then evaluate…

A: Solving the problem by finding the value of the expression.

Q: Verify the following trigonometric identity. tan(2)csc(x) = sec(x)

A:

Q: Use the double angle identities to simplify the following expressions. 10sin(5x)cos(5x) Leave your…

A:

Q: Use the adjacent figure to find the exact value of the following trigonometric function. sin 2 41 9.…

A: Explained below...

Q: Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not…

A:

Q: given that cos0=3/5, find sin0 and tan0

A: Given that the cos0=3/5.It known that the cosx=(Adjacent side)/(Hypotenuse).Here, the adjacent side…

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume…

A:

Q: Given: cosg= -, sin x= - 13, e is in the third quadrant, and x is in the fourth quadrant; evaluate…

A: Given,            cosθ=-45 , sinx=-1213 , θ is in the third quadrant and x is in the…

Q: Find the exact value by using a difference identity. tan 195°

A:

Q: Use the figure to find the exact value of the following trigonometric function. 25 20 tan 15 tan 2…

A: Applying trigonometry formula we have

Q: Without using a calculator, evaluate the following expressions as shown.

A: we know that tanθ=3 when θ=π3 for θ∈-π2,π2

Q: Complete the following table using exact values. (If an answer is undefined, enter UNDEFINED.)…

A: It is known that  csc x = 1/sin x

Q: 4. Use the given information to determine the values of the five remaining trigonometric functions.…

A:

Q: Use the given information to determine the remaining five trigonometric values. Rationalize any…

A:

Q: What is the exact value of sin (157.5°) using the half-angle identities? O v2-V2 O 2+v2 2-V2

A: We have to find the value of sin157.5°

Q: If you are going to evaluate the x²+16 using trigonometric substitution, the answer is =-csc*Ø + C,…

A:

Q: Use the given substitution to express the given radical expression as a trigonometric function…

A: Given that, From the figure of the triangle,   Apply Pythagoras theorem

Q: Find the exact value for the following. sin 105°

A: Let us assume A=45 and B=60  Then A+B=45+60=105  We will use sin(A+B)=sinAcosB+cosAsinB formula

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume…

A: For first part, Range of sine function is [-1,1] For second part, substitute x=5costheta and…

Q: Question in the file attached

A: By use Pythagorean Theorem to determine the side that would be adjacent to the angle.H2=P2+B2 .H…

Q: Find the algebraic expression for the following trigonometric expression tan(arccos 2x + arctan x²)

A: Give expression is tanarccos2x+arctanx2 We have to find the algebraic expression from…

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume…

A:

Q: 9. Use a half-angle identity to evaluate exactly sin(112.5°)

A:

Q: 9) Use half-angle identity to find the exact a Value of tan 45°

A:

Q: Use an addition or subtraction formula to write (tan33°+tan17°)/(1−tan33°tan17°) as a trigonometric…

A:

Q: Use the equivalent forms of the first Pythagorean identity If sin θ = −3/5 and θ terminates in QIII,…

A:

Q: Use a ratio identity to find tan θ given the following values. sin θ = 4, square root 17/17 and cos…

A: Given Sin θ = 41717Cos θ = 1717

Q: Make the indicated trigonometric substitution in the given algebric expression and simplify. Assume…

A:

Q: Use the power-reducing formulas to rewrite sin6 x as an equivalent expression that does not contain…

A: Given: y=sin6x for reducing power, we simplify given expression so, y=sin6x=sin3x2…

Q: Use an addition or subtraction formula to find the exact value of tan75∘

A:

Q: Create an equivalent expression for cos(x – ), using an appropriate compound angle formula

A:

Q: Find the following using all formulas from “notes" and use calculator wher necessary- 3-decimal…

A: Use the formula and use the calculator to compute the value of the sin (35°)

Q: Use the figure to find the exact value of the following trigonometric function. 25 tan 24 tan…

A: Use these formulae:

Q: Find the exact value of following expressions using half-angle formula. Do not use decimals and…

A:

Q: Use exact values to show that each of the following is true.     If tan A  = 5/12  , find tan 2 A

A: Given: A=512 The objective is to find 2A

Q: (c) Under the assumption that x = tan 0 3 sec 0, use an appropriate right triangle to tan3 + 3…

A:

Q: Find the EXACT value of sin(195°) using an addition or subtraction formula.

A:

Q: 5) sin0 × tanß sin 30° x tan 60°

A: sin30=12tan60=3

Q: What is the exact value of sin (157.5°) using the half-angle identities? 2 /2+V2

A: We need to evaluate the exact value of sin(157.5o). So,              sin157.5∘ Use the following…

Q: Use half angle formula to evaluate sin (285°)

A: Half angle formula Sin( x/2) = +√(1-cosx) /2

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify x = 2…

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.